Question

What is the prime factorization of $90$?

Answer 1

Determine the prime factorization of $90$.

Prime numbers are whole numbers greater than one that can only be divided equally by themselves and one.

Divide $90$ by only prime numbers to obtain the prime factorization.

The number $90$ is divided by $2$, which is a prime number.

$\begin{array}{rcl}90÷2& =& 45\end{array}$

Now, $45$ is divided by $3$, which is a prime number.

$\begin{array}{rcl}45÷3& =& 15\\ & \Rightarrow & 15÷3=5\end{array}$

Now, $5$ is divided by $5$, which is a prime number.

$5÷5=1$

Thus, the prime factorization of $90$ is obtained as follows:

$\begin{array}{rcl}90& =& 2\times 3\times 3\times 5\\ & \Rightarrow & 90=2\times 3^2\times 5\end{array}$

Hence, the prime factorization of $90$ is $\begin{array}{rcl}& & 2\times 3^2\times 5\end{array}$.